The impact of a lower order term in a Dirichlet problem with a singular nonlinearity (Q2211444)

Summary: In this paper we study the existence and regularity of solutions to the following Dirichlet problem \[\begin{cases} -\operatorname{div}(a(x)|\nabla u|^{p-2} \nabla u) + u|u|^{r-1} = \dfrac{f(x)}{u^{\theta}} \quad & \text{in }\Omega, \\ u > 0 & \text{in }\Omega, \\ u = 0 & \text{on }\partial\Omega \end{cases}\] proving that the lower order term \(u|u|^{r-1}\) has some regularizing effects on the solutions.